The difference in refractive index between a sample and a reference material is referred to as the differential refractive index, dRI, and is a physical parameter of considerable importance. The dRI between a sample solution consisting of a solvent plus a solute and a reference solution comprised of a pure solvent may be used to determine the solute concentration from the relation             Δ      ⁢                          ⁢      c        ≈          Δ      ⁢                          ⁢              n        /                  (                                    ⅆ              n                                      ⅆ              c                                )                      ,where the change in concentration, Δc, is directly proportional to the measured change in solution refractivity, Δn. The constant of proportionality is the reciprocal of the differential refractive index increment,             ⅆ      n              ⅆ      c        .A typical instrument for measuring the dRI is a “walk-off” type differential refractometer. That instrument contains a cell made of a transparent material with two fluid chambers, able to accommodate either a liquid or a gas, and having an angled transparent interface separating the chambers. As pictured in FIG. 1, a beam of light 1 passes into the cell, through sample chamber 2, through the interface 3 separating the two chambers, through reference chamber 4, and finally out of the cell. For the cell pictured, if the fluids in the two chambers have identical indices of refraction, then after exiting the cell the transmitted beam of light 5 travels in a path parallel to the incident beam 1. If the two fluids have different indices of refraction, then the transmitted beam of light 6 travels in a path which is at some angle θ to the incident beam. The angle θ between the incident light beam and the transmitted light beam is, to first order, proportional to the difference in refractive index between the two liquids. That angular deflection of the light beam may be measured by a variety of well established techniques, and so the dRI may be measured and reported.
Although the incident beam, as shown in FIG. 1, strikes the sample chamber interface normal to the entrance surface, in general, the incident beam will be oriented at an angle to it. In this manner, for example, it becomes possible to have the finally transmitted beam reflected by a mirror back into the flow cell chambers so that exits through the same surface. By such mirror means the sensitivity of the cell will be doubled. The emerging beam will not be parallel to or co-linear with the incident beam and may be detected more easily.
Conventionally, the angle of the transparent interface between sample and reference chambers is of the order of 45° with respect to the direction of the incident beam, though the greater this angle is the greater will be the angular deflection of the transmitted beam due to the difference between refractive indices of the sample and reference fluids. For the geometry shown, increasing this angle results in a requirement for a sample fluid chamber of increased volume while decreasing it decreases the angular deflection due to the refractive index difference between the sample and reference fluids.
Applications which utilize measurements of the dRI between two liquids typically benefit if the amount of sample required for a measurement is reduced. For many applications, sample preparation requires a great expenditure of time and resources, and reducing the quantity of sample required for measurements has a direct financial benefit. In addition to a reduction of costs and effort associated with sample preparation, the quality of measurements are in many cases enhanced if the quantity of sample required for a measurement is reduced. Liquid chromatographic systems are one example where the quality of the measurements are in some cases enhanced if the volume of sample required for measurement is reduced. In a liquid chromatographic system a material potentially consisting of many species is dissolved into a solvent and then injected into a fluid stream. The fluid stream is made to traverse some medium or device which preferentially delays species in the medium or device based upon some physical parameter, such as size, chemical affinity, thermal properties, electrical properties, etc., and so separates the species from one another. The different species thus exit the medium or device at different times. In keeping with traditional nomenclature, this medium or device will here be referred to as a column, although the physical form and function of the device may be quite different from a column. The fluid passing through the column typically exits into a small diameter tube, and so at any one moment in time different species reside at different locations along the length of the tube. If a measurement device, such as a differential refractometer, is situated such that the fluid flows from that tube through the measurement device, then the species which make up the material may be individually measured. The measurement of constituent species of a material is an essential purpose of chromatographic systems. Since a finite volume of liquid is always required for measurement, the species within some volume of the tube necessarily contribute to the signal at any moment in time. The measurement device is therefore always measuring an average over the species which reside along the length of the tube which corresponds to the measurement volume. This averaging over species negates in part the separation accomplished by the column, and results in a reduction in the quality of data. Reducing the volume of sample required for measurement minimizes the averaging over species, resulting in higher quality data.
In addition to the negative effects on data quality due to the measurement averaging over a finite volume of sample, some volume of sample is mixed together as it traverses the measurement system. Many chromatographic systems consist of several measurement devices placed serially along the fluid stream, each measuring different physical parameters concerning the sample. If a measurement device mixes some volume of fluid together, then all subsequent measurements on that fluid are negatively impacted by the resulting averaging over multiple species in the measurement volume. Typically, the larger the volume required for measurement, the larger the volume of sample which is mixed together, and the greater the negative impact on data quality for instruments placed later in the fluid stream.
In addition to their application in the field of liquid chromatography, differential refractometers of various types are used in many different fields. By accurately determining refractive index differences between a reference standard and a sample, such determinations may be used to determine sucrose concentration, fluid densities, the concentrations of a myriad of industrial fluids such as sulfuric acid, sodium chloride, ethanol, etc. A variety of instruments have been designed around the concept of measuring and using such refractive index differences as a means to measure various derivative quantities.
There are clearly advantages in reducing the volume of sample required for a dRI measurement. However, for a walk-off type differential refractometer, a tradeoff exists between reduction of the sample volume and sensitivity of the dRI measurements. There are at least three reasons for a reduction in dRI sensitivity with a reduction in sample volume. The first reason for a reduction in sensitivity is a reduction in averaging over the sample. For even perfectly stable systems, fundamental laws of thermodynamics predict local fluctuations through time of the temperature, density, and solute concentrations across the sample and reference liquids. This was explained at length by Albert Einstein in his 1910 seminal paper on “The theory of opalescence of homogeneous fluids and liquid mixtures near the critical state,” published in Annelen der Physik, volume 33, pages 1275–1298. Real world systems are never perfectly stable, and those fluctuations are in general enhanced in real systems. Those fluctuations cause the path of the light beam traversing the fluids to change through time, and so cause the angle θ at which the light beam 6 exits the cell to fluctuate with time. The fluctuations through time of the beam angle are seen as noise in the dRI measurement. Increasing the volume sampled by the beam causes the beam to better average over these local fluctuations, reducing their overall effect.
A second reason that a reduction in sample volume results in a reduction in sensitivity of the dRI measurement is a reduction of optical power through the system. For the cell design picture in FIG. 1, as the sample volume is reduced, the area of sample through which light may be sent is reduced. To obtain the same optical power through the system, the light intensity must be increased. Typically, a system used to measure the angular deflection of the light beam has its sensitivity increase in some proportion to the optical power supplied to it. Therefore, to obtain with a smaller volume sample the same sensitivity in the determination of the beam angular deflection as with a larger volume sample, the light intensity must be increased. Since these systems are typically already using the most intense light sources practicable, a reduction in sample volume necessarily results in a reduction of optical power through the system and a corresponding reduction in the sensitivity with which the angular deflection of the light beam may be determined. A reduction in the sensitivity with which the angular deflection of the light beam may be determined corresponds directly to a reduction in sensitivity of the dRI measurement.
A third way that reducing sample volume reduces sensitivity of the dRI measurement is once again due to a reduction in the area through which the light beam may be sent. As the area through which the light beam is sent is reduced, diffraction effects limit the sharpness with which the beam may subsequently be focused. The smaller the area through which the beam passes, the more diffuse the focal point becomes. Typically, a system used to measure the angular deflection of the light beam has its sensitivity increase as the sharpness of the focused beam increases. And so yet again reducing the area through which the light beam passes results in a decrease in sensitivity in determining the beam angular deflection, corresponding to a reduction in sensitivity of the dRI measurement.
It is an important objective of my invention to increase the sensitivity of a dRI measurement while at the same time minimizing the amount of sample required. Another objective of my invention is to reduce diffraction effects by increasing the dimension of the clear aperture through which the beam must pass without increasing the sample volume. A further objective is to provide for a broad range of instrument response without the beam moving too closely to any side of the cell.